Transcript Document
Everyday Benefits of Understanding Variability Larry Weldon Statistics and Actuarial Science Simon Fraser University Canada Missed Opportunity ? Formal Inference H0 p-value, … Informal Application Of Statistical Thinking Stats Teachers And Consultants Formal Inference H0 p-value, … Students and Consultees General Public Usefulness of Informal Stats Examples from … • • • • • Sports Investment Peer Review Health Lotteries Need for Communication without Math Ordinary Language & Graphs Sport – the quality illusion • • • • • • Role of Luck in Game Outcomes Teams closely matched Short-run results mislead Illusion that winning team is “better” Bigger payoff when underdog wins Bet the underdog! Sport – when variability is the key • • • • • Golf: Describing difficulty of holes Par is not a good measure of difficulty Variability of strokes is better Nicklaus Comment (Clarke(2007)) Role of Luck … Investment – Back-the-winner fallacy • Mutual Funds - a way of diversifying a small investment • Which mutual fund? • Look at past performance? • Experience from symmetric random walk … Trends that do not persist Random Walk with Slight Trend - best ones obvious? • Funds tend to mimic market indexes • Use 5-year performance to select ‘best’ • Check relative performance of ‘best’ compared to rest. • Assume simulated quality of fund used for past 5 yrs is used for next 5 yrs. START = 100 Mutual Fund Advice? Don’t expect past relative performance to be a good indicator of future relative performance. Investment – variability vs risk • Risk - probability of loss Versus • Risk - variability of returns Equities Win With Prob = .97 Bonds “risky”! Investment Mix Advice? • Depends on time horizon • Not only tolerance for variability • Long term - 100% equities • Short term - mix equities & bonds Research – the randomness of peer review - study via simulation • Average referees accept 20% of average quality papers • Referees vary in accepting 10%-50% of average papers • Two referees accepting a paper -> publish. • Two referees disagreeing -> third ref • Two referees rejecting -> do not publish Beta(2,2) Beta(3,12) 6 Ultimately published: 6 + .20*13 (approx) 13 =9 papers out of 100 16 others just as good! 6 Peer Review Flawed • Does select good papers but • Is unfair in this selection … • Similar property of school admission systems, competition review boards, etc. Health – mimicking the natural environment • • • • Variability - often called “error” Is it always bad? Quirky example - Brewster (2005) Random variability of oxygen supply on respirator more viable than constant supply. • Variability is “natural”! Lotteries – expectation and hope • Cash flow – Ticket proceeds in (100%) – Prize money out (50%) 50 % – Good causes (35%) – Administration and Sales (15%) •$1.00 ticket worth 50 cents, on average •Typical lottery P(jackpot) = .0000007 How small is .0000007? • Buy 100 tickets every week for 60 years • Cost is $312,000. • Chance of winning jackpot is = …. 2 percent! Other Negatives • Inflation decreases value of jackpot relative to ticket value • Jackpot may need to be shared by others with same numbers on ticket Positives? • Fun to hope and dream? • Maybe other vehicles with better odds Overview • Some real-life processes better understood with statistical knowledge • Little known effects can be made understandable to general public • Professional statisticians should convey these effects to the public • Perhaps statistics better appreciated Thank you for listening